In 1912, two years after her death at 90, a statue of Florence Nightingale was erected on Waterloo Place, London. The Times reported that the statue's face reflected 'characteristic qualities of strength of will irradiated by an expression of great sweetness and sympathy'. The image of the heroine of Scutari, the mother of the nursing sisterhood, the ministering angel of the Crimea, had become a model of Victorian womanhood - thereby reducing the life of a quite exceptional woman to an ideal of nurturing femininity.

In this fascinating biography, written with clear-eyed respect and affection for its subject, Mark Bostridge examines and dismantles the many myths, both hagiographical and debunking, that have hardened like barnacles around the real story of Florence Nightingale. The rumour, for example, that she suffered syphilis gets short shrift, as do claims, based on a youthful correspondence full of flowery endearments, that she was a lesbian. Bostridge steers a firm course between the Florence favoured by her devotees - the Lady with the Lamp - and the cold, inhuman number-cruncher of the revisionists. In doing so, he returns us to the enormity of the real woman's achievements.

By sheer will and an intellect that combined creativity and detailed analysis, Nightingale changed the way we perceive public health. Once she had started on her mission, she never stopped: when crippled by excruciating brucellosis, bed-bound for decades, she set about writing a vast report on 'improving the health of India'. Even the best-known of her early detractors, Lytton Strachey, who decided her energy could only be the result of repressed erotic urges, was forced into admiration for her achievements. It was what he perceived as her 'religiosity' that he found repellent, and he sniggered that 'in some of her speculations she seems hardly to distinguish between the Deity and drains'.

Bostridge is particularly good on Florence's religious faith, and he has read widely among the influences and ideas that informed it. Though she said she was inspired by the voice of God calling her in her youth, her deep religious belief was mystical, unorthodox and free of any taint of religiosity. It had little to do with church or piety, or even Christ. On both sides, the Nightingales were of dissenting stock, and she was brought up among free-thinking, intellectually adventurous Unitarians who enjoyed a stimulating combination of public purpose and private inquiry. She disliked religious ritual and seemed not to ally herself with any denomination; it was science that illuminated divine purpose to her, and in particular the new discipline of statistics, which she considered, as Bostridge puts it, 'a sacred science which could permit man to read the mind of God'. One of her unsung legacies is the popularisation of statistical data by the use of pie-charts and diagrams.

Other well-known Nightingale narratives are re-examined by Bostridge - and many are at least half discarded. Her mother, Fanny, is not here the caricature of popular legend, the social-climbing tyrant who bound her to a relentless round of balls, light philanthropy and netting purses. Florence's elder sister, Parthenope, is still tiresome, with her debilitating, monomaniacal obsession with her brilliant sibling; but she is not absurd. This is a much more rounded, complex and plausible picture of the conditions in which Florence's extraordinary personality came to fruition.

There is something unnerving - something strange and therefore interesting - in the intensity of the young Florence's desire to do something; her determination, adhered to at painful cost, to remain unmarried in order to fulfil a destiny which was at that point still cloudy to her. She was not interested in saints but she has some of the characteristics associated with sainthood - none of them anything to do with being nice.

From Bostridge's careful account, we can begin to imagine what Fanny Nightingale, an intelligent woman, might have feared in her daughter's ambitions. Aged six, Florence was making graphs on the efficacy of prayer; aged nine, she was reading Homer in Greek. By her early twenties she was corresponding on philosophy, theology and sanitation with some of the most powerful thinkers and public servants of her time - friends and guests of her parents - including Sidney Herbert, who as Secretary of War was to commission her 15 years later to lead 40 nurses to the Barrack Hospital at Scutari. Bostridge doesn't labour the point but he does convincingly demonstrate that the world of the Victorian woman born into a wealthy family with a respect for the life of the mind was not wholly the spiral of 'busy nothings' that Parthenope once described it as.

Bostridge's portrait of Florence herself is also even-handed and sympathetic. She emerges as a lover of humanity rather than a lover of individual humans, with a mind that could scythe through obfuscating bureaucratic reports on hospital conditions or the iniquitously inefficient Poor Laws, which had rotted deep into the 19th-century social psyche. She bore long grudges, enjoyed intrigue and, despite her lamplit patrols among the wounded at Scutari, had, as her friend the poet Arthur Clough put it, 'a high, steady benevolence' rather than the warmth of human empathy. Though her prodigious cleverness and engagement had dazzled when she was young, in celebrated middle-age she was formidable rather than charming - even her loyal Aunt Mai described her as 'often cold and dry, some might say cross'.

Mark Bostridge has produced a fine study of a complex and remarkable woman. There will be other lives of Florence Nightingale but it is hard to imagine one that brings her hard, driven brilliance back to life with such intelligence, imagination and sympathy.